Thecogencyoftheargumentdependsupontheapplicabilityoftheruletothefact。Ifmenbenotmortal，or，again，ifSocratesbenotaman，theinferenceisnotvalid；andthesetwodistinctissues，theissueoflawandtheissueoffact，mayberaisedinanycase。27*Thevalueofthesyllogismisthatitraisestheseissuesdistinctly。Theargumentisthusputinsuchaformastobeabsolutelyconclusiveifthepremisesbethemselvesgranted。
Itthereforeprovidesatestofthevalidityofthelogic。
Grantingthepremises，adenialoftheinferencemustinvolveacontradiction。Thatistheonlytestinpurelogic。Thesyllogismmust，therefore，beinasensetautologous，forotherwiseitcouldnotbeconclusive。Acceptanceo？thepremisesmustbeshownfromtheformofstatementtonecessitatetheadmissionoftheinference。Thisfollows，andthelogicallinkiscompleteandirrefragable，ifthemiddletermbeidenticalinbothpremises，andnototherwise。ThisiswhatMillindicatesbysayingthat’therulesofthesyllogismarerulesforcompellingapersontobeawareofthewholeofwhathemustundertaketodefendifhepersistsinmaintaininghisconclusion。’28*Ratiocination，ashesumsuphisviewelsewhere，’doesnotconsistofsyllogisms’；
butthesyllogismisausefulformulaintowhichitcan’translateitsreasonings，’andsoguaranteetheircorrectness。29*Ifthisbegranted，wemustconsidertheessentialstepofinferencetobeembodiedin，butnotcreatedby，thesyllogism。Correctreasoningcanalwaysbethrownintothisform。Thesyllogismemergeswhenthereasoningiscomplete。
’Theuseofthesyllogismisnoother，’saysMill，’thantheuseofgeneralpropositionsinreasoning。’Itisasecurityforcorrectgeneralisation。30*Wehave，then，stilltoaskwhatisthereasoningprocessforwhichthesyllogismprovidesatest。